   Chapter 2.4, Problem 15E

Chapter
Section
Textbook Problem

In Exercises 9-16, complete the table by computing f(x) at the given values of x. Use these results to estimate the indicated limit (if it exists).15. f ( x ) = x 2 + x − 2 x − 1 ; lim x → 1 f ( x ) x 0.9 0.99 0.999 1.001 1.01 1.1 f(x)

To determine
The values of f(x) at different values of x and estimate the indicated limit.

Explanation

Given:

The given function is f(x)=x2+x2x1 and the limit is limx1f(x) .

Calculation:

Use factorization method to simplify the given function.

f(x)=x2+2xx2x1=x(x+2)1(x+2)x1=(x1)(x+2)x1(Cancelthecommonfactors)=x+2

The simplified function is,

f(x)=x+2 (1)

Find the values of f(x) for different values of x.

Substitute 0.9 for x in equation (1) to find the value of f(x) .

f(0.9)=0.9+2=2.9

Substitute 0.99 for x in equation (1) to find the value of f(x)

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